Method and apparatus for biosensor spectral shift detection

ABSTRACT

Performing high-resolution determination of the relative shift of the spectral properties of a biosensor. The shift in the resonance peak of the biosensor is indicative of the amount of material bound to the surface of the biosensor. A preferred biosensor is a Guided Mode Resonant Filter Biosensor (GMRFB). In one aspect of the invention, curve fitting is used to determine the relative location of the spectrum of the unexposed biosensor with respect to those spectra that are altered (e.g., shifted) by the presence of materials bound to the surface of the biosensor. In an alternative embodiment, the cross correlation function is used to detect spectral peak offsets between a reference spectrum and a spectrum measured from an exposed biosensor. In yet another alternative, maximal likelihood estimation techniques are used to determine the spectral shift or offs.

This application is a Continuation-In-Part of U.S. patent applicationSer. No. 10/059,060 filed Jan. 28, 2002 now U.S. Pat. No. 7,070,987 anda Continuation-In-Part of U.S. patent application Ser. No. 10/058,626filed Jan. 28, 2002 now U.S. Pat. No. 6,951,715, both of which areContinuations-in-Part of U.S. patent application Ser. No. 09/930,352,filed Aug. 15, 2001 now U.S. Pat. No. 7,094,595, which claims thebenefit of U.S. provisional application 60/244,312 filed Oct. 30, 2000,U.S. provisional application 60/283,314 filed Apr. 12, 2001, and U.S.provisional application 60/303,028 filed Jul. 3, 2001, all of which arehereby incorporated by reference.

BACKGROUND OF THE INVENTION

A. Field of the Invention

The present invention relates to biosensors useful for detectingbiological material. More specifically, it is directed to a method anddevice for determining the amount of shift in an optical biosensor'sspectral output.

B. Description of the Related Art

With the completion of the sequencing of the human genome, one of thenext grand challenges of molecular biology will be to understand how themany protein targets encoded by DNA interact with other proteins, smallmolecule pharmaceutical candidates, and a large host of enzymes andinhibitors. See e.g., Pandey & Mann, “Proteomics to study genes andgenomes,” Nature, 405, p. 837–846, 2000; Leigh Anderson et al.,“Proteomics: applications in basic and applied biology,” Current Opinionin Biotechnology, 11, p. 408–412, 2000; Patterson, “Proteomics: theindustrialization of protein chemistry,” Current Opinion inBiotechnology, 11, p. 413–418, 2000; MacBeath & Schreiber, “PrintingProteins as Microarrays for High-Throughput Function Determination,”Science, 289, p. 1760–1763, 2000; De Wildt et al., “Antibody arrays forhigh-throughput screening of antibody-antigen interactions,” NatureBiotechnology, 18, p. 989–994, 2000. To this end, tools that have theability to simultaneously quantify many different biomolecularinteractions with high sensitivity will find application inpharmaceutical discovery, proteomics, and diagnostics. Further, forthese tools to find widespread use, they must be simple to use,inexpensive to own and operate, and applicable to a wide range ofanalytes that can include, for example, polynucleotides, peptides, smallproteins, antibodies, and even entire cells.

For the majority of assays currently performed for genomics, proteomics,pharmaceutical compound screening, and clinical diagnostic applications,fluorescent or colorimetric chemical labels are commonly attached to themolecules under study so they may be readily visualized. Becauseattachment of a label substantially increases assay complexity andpossibly alters the functionality of molecules through conformationalmodification or epitope blocking, various label-free biosensortechnologies have emerged. Label-free detection phenomenologies includemeasuring changes in mass, microwave transmission line characteristics,microcantilever deflection, or optical density upon a surface that isactivated with a receptor molecule with high affinity for a detectedmolecule. The widespread commercial acceptance of label-free biosensortechnologies has been limited by their ability to provide high detectionsensitivity and high detection parallelism in a format that isinexpensive to manufacture and package. For example, biosensorsfabricated upon semiconductor or glass wafers in batchphotolithography/etch/deposition processes are costly to produce andpackage if the sensor area is to be large enough to contain largenumbers of parallel assays. Similarly, the requirement of makingelectrical connections to individual biosensors in an array posesdifficult challenges in terms of package cost and compatibility withexposure of the sensor to fluids.

Biosensors have been developed to detect a variety of biomolecularcomplexes including oligonucleotides, antibody-antigen interactions,hormone-receptor interactions, and enzyme-substrate interactions. Ingeneral, biosensors consist of two components: a highly specificrecognition element and a transducer that converts the molecularrecognition event into a quantifiable signal. Signal transduction hasbeen accomplished by many methods, including fluorescence,interferometry (Jenison et al., “Interference-based detection of nucleicacid targets on optically coated silicon,” Nature Biotechnology, 19, p.62–65; Lin et al., “A porous silicon-based optical interferometricbiosensor,” Science, 278, p. 840–843, (1997)), and gravimetry (A.Cunningham, Bioanalytical Sensors, John Wiley & Sons (1998)).

Of the optically-based transduction methods, direct methods that do notrequire labeling of analytes with fluorescent compounds are of interestdue to the relative assay simplicity and ability to study theinteraction of small molecules and proteins that are not readilylabeled. Direct optical methods include surface plasmon resonance (SPR)(Jordan & Corn, “Surface Plasmon Resonance Imaging Measurements ofElectrostatic Biopolymer Adsorption onto Chemically Modified GoldSurfaces,” Anal. Chem., 69:1449–1456 (1997), grating couplers (Morhardet al., “Immobilization of antibodies in micropatterns for celldetection by optical diffraction,” Sensors and Actuators B, 70, p.232–242, 2000), ellipsometry (Jin et al., “A biosensor concept based onimaging ellipsometry for visualization of biomolecular interactions,”Analytical Biochemistry, 232, p. 69–72, 1995), evanascent wave devices(Huber et al., “Direct optical immunosensing (sensitivity andselectivity),” Sensors and Actuators B, 6, p. 122–126, 1992), andreflectometry (Brecht & Gauglitz, “Optical probes and transducers,”Biosensors and Bioelectronics, 10, p. 923–936, 1995). Theoreticallypredicted detection limits of these detection methods have beendetermined and experimentally confirmed to be feasible down todiagnostically relevant concentration ranges. However, to date, thesemethods have yet to yield commercially available high-throughputinstruments that can perform high sensitivity assays without any type oflabel in a format that is readily compatible with the microtiterplate-based or microarray-based infrastructure that is most often usedfor high-throughput biomolecular interaction analysis. Therefore, thereis a need in the art for compositions, biosensors, methods of preparingbiosensors and analytical methods that can achieve these goals.

Guided Mode Resonant Filter Biosensors (GMRFBs) have been shown to beone such biosensor well-suited to determining the degree to whichbiomolecular interactions are taking place near the sensor surface,without resorting to labeling techniques (including fluorescence,calorimetric, and radiolabeling). GMRFBs also excel at monitoringinteractions involving small molecules, proteins, cells, microorganisms,and viruses.

Thus, there exists a need for robust methods of determining the relativeshifts of the biosensor spectra. Preferably, such an algorithm candetect spectral changes even when the spectral characteristics of thebiosensor do not exhibit a clearly defined peak, or if it has multiplepeaks.

SUMMARY OF THE INVENTION

A method and apparatus for performing high-resolution determination ofthe relative shift of the spectral properties of a biosensor isprovided. The shift in the resonance peak of the biosensor is indicativeof the amount of material bound to the surface of the biosensor. Theapparatus may be used with a colorimetric resonant biosensor having asurface of amine functional groups useful for attaching biologicalmolecules. A preferred biosensor is a Guided Mode Resonant FilterBiosensor (GMRFB).

In one embodiment, parametric fits to the observed resonance peak areused to estimate the exact location of the peak. Peaks thusly obtainedover time are subtracted from one another to determine spectral shifts.

In another embodiment, the cross correlation function is used todetermine the relative location of the spectrum of the unexposedbiosensor with respect to those spectra that are altered (e.g., shifted)by the presence of materials bound to the surface of the biosensor. Theoriginal spectral measurements or other biosensor reference data areused to generate digital filter coefficients, which are then used toprocess the subsequent spectral measurements. The filter thus operatesas a correlation-based matched filter that provides a peak output at anoffset, the offset indicating the amount of spectral shift between thereference spectrum and the altered spectrum.

Alternative embodiments may include obtaining a number of measurementsof the exposed biosensor, filtering each set of altered spectralmeasurements with the matched filter to obtain a correlation signal, andthen averaging the correlation signals. Alternatively, the measurementsare first averaged and the averaged signal is then processed with thematch-filter. If the measurements are taken over a period of time, thentime-based trends of resonance shift may be analyzed. Further, thecorrelation results may then be analyzed with a peak finding algorithmor curve fitting algorithm to locate the correlation peak indicative ofthe resonance shift.

Still further embodiments identify the spectral shift of the resonancepeak by examining the slope of the magnitude of the spectral response(rate of change of the magnitude with respect to frequency). This mayinclude (i) determining at least two reference frequencies around whichthe slope of the response has the highest magnitudes (ii) using testdata, determining at least two test frequencies around which the slopeof the response has the highest magnitudes; and (iii) determining theshift of the peak in response to the at least two reference frequenciesand at least two test frequencies.

BRIEF DESCRIPTION OF THE DRAWINGS

The objects, features and advantages of the present invention will bemore readily appreciated upon reference to the following disclosure whenconsidered in conjunction with the accompanying drawings, in which:

FIG. 1 depicts a preferred embodiment of the instrumentation used toilluminate and read the output of a biosensor;

FIG. 2 shows an array of detector devices used to record spectral data;

FIG. 3 shows a graph of the relationship between the spectral binnumbers and the spectral wavelengths;

FIG. 4 shows a graph of the relationship between the bin numbers and thespectral width of the bins;

FIG. 5 shows the relationship depicted in FIG. 4 in more detail;

FIG. 6 shows a typical spectral resonance of a biosensor;

FIG. 7 shows a region of the spectral resonance;

FIG. 8 shows correlation data;

FIG. 9 shows a plot of resonance peak spectra derivative values; and

FIGS. 10, 11, and 12 show methods of determining resonance peak offsets.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The preferred calorimetric resonant optical biosensor allows biochemicalinteractions to be measured on the sensor's surface without the use offluorescent tags or calorimetric labels. The sensor surface preferablycontains an optical structure that, when illuminated with collimatedwhite light, is designed to reflect only a narrow band of wavelengths.The narrow wavelength band is described as a wavelength “peak.”

One preferred guided mode resonant filter structure is a one-dimensionallinear grating surface structure. The sensor can be manufactured byperforming sub-micron definition of grating features usingphotolithography on the sensor. Alternatively, the sensor can beproduced inexpensively over large surface areas using sub-micronmicroreplication of a master sensor surface structure on continuoussheets of plastic film. Alternative structures, including 2-D or 3-Dstructures, surface relief structures, glass substrates, discreteplastic film, as well as alternative fabrication methods, may also beused.

The sensor structure can incorporated into standard microtiter platesand used to perform affinity assays based on measuring the biochemicalinteraction between a substance immobilized on the sensor surface(molecule, peptide, protein, DNA, RNA, phage, cell, bacteria, polymer)and substances within a test sample. The sensor can also be incorporatedinto other disposable laboratory assay formats, such as microarrayslides, flow cells, and cell culture plates. The plastic sensors may beincorporated into the bottoms of bottomless microtiter plates (e.g.,microtiter plates having any number of wells, preferably 6, 24, 48, 96,384, 1536, or 3456 wells), as well as microarrays, and microfluidicdevices. These sensor platforms may be used the sensor plate to performmultiple protein-protein binding assays in parallel.

When molecules are attached to the surface of the sensor, the reflectedwavelength (color) is shifted due to the change of the optical path oflight that is coupled into the grating. By linking receptor molecules tothe grating surface, complementary binding molecules can be detectedwithout the use of any kind of fluorescent probe or particle label. Thedetection technique is capable of resolving changes of ˜0.1 nm(nano-meter) thickness of protein binding, and can be performed with thegrating surface either immersed in fluid or dried.

The readout system preferably consists of a white light lamp thatilluminates a small spot of the grating at normal incidence through afiber optic probe, and a spectrometer that collects the reflected lightthrough a second fiber, also at normal incidence. Because no physicalcontact occurs between the excitation, readout system and the gratingsurface, no special coupling prisms are required and the grating can beeasily adapted to any commonly used assay platform, including microtiterplates and microarray slides. A single spectrometer reading is performedin several milliseconds, thus it is possible to quickly measure a largenumber of molecular interactions taking place in parallel upon a gratingsurface, and to monitor reaction kinetics in real time. Alternatively,imaging spectrometers can also be used.

It is expected that this system will be most useful in applicationswhere large numbers of biomolecular interactions are measured inparallel, particularly when molecular labels will alter or inhibit thefunctionality of the molecules under study. High throughput screening ofpharmaceutical compound libraries with protein targets, and microarrayscreening of protein-protein interactions for proteomics are examples ofapplications that require the sensitivity and throughput afforded bythis approach.

A schematic diagram of a preferred system used to illuminate the sensorand to detect the reflected signal is shown in FIG. 1. The sensordepicted in FIG. 1 includes a substrate, a grating surface or region,and liquid chambers to isolate the well. The chamber walls arepreferably arranged in a grid pattern to provide isolated regions, orwells, in which reactions may take place. Therefore, each individualwell functions as a separate biosensor. A spectrometer, connected to anoptical probe head, is used to measure the reflected light. The probehead contains two optical fibers—an illuminating fiber and a detectionfiber. In this embodiment, a white light source illuminates a ˜1 mmdiameter region of the grating surface through a 100 micrometer diameterfiber optic and a collimating lens at nominally normal incidence throughthe bottom of the microtiter plate. The white light source may beincorporated into the spectrometer, or may be supplied by a separatedevice.

After passing through the collimating lens, incident light passesthrough a linear polarizing filter so that the linear grating is excitedonly with light that is polarized either parallel or perpendicular tothe grating lines. Reflected light passes through the polarizing filteragain on its way back to the detection probe. A detection fiber isbundled with the illumination fiber for gathering reflected light foranalysis with the spectrometer. One suitable spectrometer for use in thesystem of FIG. 1 is an HR 2000 High Resolution Spectrometer, which maybe obtained from Ocean Optics, at 380 Main Street, Dunedin, Fla., 34698.

In one preferred embodiment, a series of 8 illumination/detection headsare arranged in a linear fashion, so that reflection spectra aregathered from all 8 wells in a 96-well (generally arranged as 8-rows by12-columns) microtiter plate column at once. The microtiter plate sitsupon a motion stage so that each column can be addressed in sequence.The instrument is currently capable of measuring all 96 wells inapproximately 15 seconds, limited by the movement rate of the motionstage.

A spectrophotometer typically measures light intensity at variouswavelengths. A block diagram of various components of aspectrophotometer 200 are depicted in FIG. 2. The magnitude of the lightmay be measured by reflecting the incoming light 202 to be measured offa diffraction grating 204, which acts as a prism. The diffractiongrating 204 spreads the received light based on its wavelength, therebyseparating it into its constituent components indicated by light rays206. The spread, or distributed, light is then applied to a sensor 208made up of a linear array of light sensitive elements or detectors 210(charge-coupled devices, or CCDs) each of which measures and records themagnitude of the incident light at that CCD element. Typicalspectrometers use 2048 CCD elements or pixels. The output 212 from thesensor 208, or CCD array, corresponds to a sampled version of thereflected spectral energy. The output is typically provided over adigital communication link such as an I²C data bus, USB data bus, orequivalent, in the form of a data array.

Numerous factors affect the accuracy of the spectrometer output 212. Thegrating 204 typically spreads the light approximately one degree pernanometer of wavelength. As can be seen in FIG. 2, the light is notevenly spread onto the linear array. This can be corrected for bycurving the linear array of CCDs so that light is distributed moreevenly. Alternatively, bins on the outer regions can be made larger tocorrespond to the same bandwidth. Nevertheless, imperfections in theplacement of the CCD sensor array, and imperfections in the size andplacement of the CCD elements within the array may affect the accuracy.In addition, imperfections in the grating will result in non-uniformdistribution of the light constituents. Still further, quantizationerrors may be present due to the sampling process.

Each CCD may be considered a wavelength “bin” such that all of thedistributed light components which fall onto that CCD element areaccumulated and represented as a single value that is output from thatCCD element. It can be seen that the width of the CCD element affectsthe range of wavelengths (frequency bandwidth) that will be incident toit. Ideally, all such bins will have a uniform bandwidth resulting inuniform wavelength quantization. Additionally, the bins are preferablyuniformly spaced.

In practice, however, most spectrometers do not have bins with uniformwidth and spacing. In particular, most spectrometers provide acalibration mechanism to account for any measurable errors so that theymay provide the most accurate data output 212 as possible. For example,the above-referenced HR 2000 spectrometer relates the wavelength of agiven pixel to a third order function of the pixel number. Calibratedspectrometers typically provide spectral data in output 212corresponding to non-uniformly spaced wavelength bins. In this case, thedata output 212 also includes data values indicating the spacing of thespectral data. In one preferred embodiment, the data 212 includes twodata arrays, one array containing spectral magnitude data values, andone array having corresponding bin center wavelengths (or frequencies).

As seen in FIG. 3, the relationship between wavelength and bin number isnot linear, indicating the bin width is not uniform. The shape of thecurve indicates that higher bin numbers have smaller bin widths. Thiscan be seen more clearly in FIG. 4, which shows the bin width, orresolution, as a function of bin number. Low numbered bins have a widthof approximately 0.16 nanometers, while higher numbered bins have abandwidth of approximately 0.1 nanometers. FIG. 5 shows a smaller regionof FIG. 4 (from bin 625 to bin 925), indicating another aspect of thequantization noise. For example, for bins 625 through 650, the bandwidthindicted by the spectrometer oscillates between 0.141 and 0.142nanometers. This is due to the finite resolution provided by thespectrometer, and results in quantization error.

Spectral Data Interpolation

In some spectral shift detection embodiments, the signal processing usedto identify the shift in the peak resonance frequency operates moreaccurately when the spectral samples are spaced uniformly. Thus, in theevent the data 212 from the spectrometer 200 corresponds to non-linearlyspaced wavelengths, the data 212 is preferably linearized via aninterpolation routine. Numerous interpolation methods can be used,including linear, quadratic, cubic, splines, or digital FIR or IIRfiltering of the spectral data points with appropriate zero filling,etc. One preferred interpolation method is piecewise cubic Hermiteinterpolation. One such piecewise cubic Hermite interpolation routine isfound in the Matlab simulation software program, available from TheMathWorks, Inc., 3 Apple Hill Drive, Natick, Mass., 01760, as set forthbelow:

INTERP1 1-D interpolation (table lookup).

-   -   YI=INTERP1 (X, Y, XI) interpolates to find YI, the values of the        underlying function Y at the points in the vector XI.    -   The vector X specifies the points at which the data Y is given.        If Y is a matrix, then the interpolation is performed for each        column of Y and YI will be length(XI)-by-size(Y,2). Out of range        values are returned as NaN.    -   YI=INTERP1 (Y,XI) assumes X=1:N, where N is the length(Y) for        vector Y or SIZE(Y,1) for matrix Y.    -   Interpolation is the same operation as “table lookup”. Described        in “table lookup” terms, the “table” is [X,Y] and INTERP1        “looks-up” the elements of XI in X, and, based upon their        location, returns values YI interpolated within the elements of        Y.    -   YI=INTERP1(X,Y,XI,‘method’) specifies alternate methods. The        default is linear interpolation. Available methods are:        -   ‘nearest’—nearest neighbor interpolation        -   ‘linear’—linear interpolation        -   ‘spline’—cubic spline interpolation        -   ‘cubic’—cubic interpolation    -   All the interpolation methods require that X be monotonic. X can        be non-uniformly spaced. For faster interpolation when X is        equally spaced and monotonic, use the methods ‘*linear’,        ‘*cubic’, ‘*nearest’. For faster linear interpolation when X is        non-uniformly spaced see INTERP1Q.    -   For example, generate a coarse sine curve and interpolate over a        finer abscissa:        -   x=0:10; y=sin(x); xi=0:25:10;        -   yi=interp1(x,y,xi); plot(x,y,‘o’,xi, yi)        -   See also INTERP1Q, INTERPFT, SPLINE, INTERP2, INTERP3,            INTERPN.

Typically, the preferred interpolation routine operates on the two datavectors (each vector being a one-dimensional array) representing thewavelengths (vector X) and the corresponding spectral magnitudes (vectorY) from the spectrometer. The interpolation routine is also providedwith a vector representing the linearly spaced wavelengths (vector XI)for which interpolated spectral magnitude data is desired. Theinterpolation routine then returns the interpolated values (vector YI)for the spectral magnitudes at the desired wavelengths (given by XI). Inone embodiment, a data array of 2048 values may be interpolated into24,000 values. More or fewer interpolated points may be used. Theinterpolated data is then processed to determine the wavelengthcorresponding to the maximum reflected energy, as discussed below.Sample spectra are shown in FIG. 6. FIG. 7, which depicts the data fromFIG. 6 between 863.5 to 863.7 nanometers, shows the “raw” data from thespectrometer as curve 702, while the interpolated data is shown in curve704.

Resonant Peak Determination Using Curve Fitting

In this embodiment, the resonance peaks are determined by fitting curvesto the measured spectral data. The curves are then used to determine thepeak resonance analytically, preferably using the characteristics of thecurves (e.g., locating the point x_(p) where the curve's derivative iszero, e.g., for the curve ax²+bx+c, where x_(p)=−b/2a).

Typically, a reference curve is determined from data representing thespectral resonance of an unexposed biosensor. The reference curve may beobtained from spectral data representing an average of a number ofspectral measurements to decrease the noise inherent in the measureddata. The reference may be obtained from the actual biosensor in use, ormay be data obtained from a prototypical biosensor and stored in thesystem for future use.

Then, spectral data is gathered from an exposed biosensor. The curvefitting is separately performed on the spectral data from the exposedbiosensor, and the curve characteristics are then used to locate thepeak of the shifted spectra. The shift of the peak resonance is thendetermined by comparing the peak of the reference curve and the peak ofthe shifted curve obtained from the exposed biosensor.

Preferably the entire set of spectral measurements is not used. Therange of data (or “window”) used in the curve fitting method may bedetermined using any suitable criteria, such as a predetermined range ofwavelengths on either side of the absolute maximum peak value, or arange of wavelengths based on a multiple (e.g., 1.0, 1.5, etc.) of thehalf power bandwidth (or any other suitable relative power measurement,such as the one third or one quarter power bandwidth), etc. The user mayalso select a range of wavelengths by providing input by way of a GUI orcommand-line prompt. In another preferred embodiment, turning points ofthe spectrum may be used to identify the relevant spectrum. A turningpoint is a point where the slope of the spectral response is zero (or apoint where the slope is non-monotonic, changing from increasing valuesto decreasing values, or vice-versa). Preferably the peak is determinedand the spectral data surrounding the peak is examined for monotonicity(or alternatively, for zero slope). The spectral data may first besmoothed (e.g., by filtering the data points) prior to identification ofthe turning points that may be used to define the edges of the resonantpeak.

The first analytic curve examined is a second-order polynomial, given byy=ax ² +bx+c

The least-squares solution to this equation is given by the costfunction

${\phi = {\sum\limits_{i = 1}^{n}\left( {{a\; x_{i}^{2}} + {b\; x_{i}} + c - y_{i}} \right)^{2}}},$the minimization of which is imposed by the constraints

$\frac{\partial\phi}{\partial a} = {\frac{\partial\phi}{\partial b} = {\frac{\partial\phi}{\partial c} = 0.}}$

Solving these constraints for a, b, and c yields

$\begin{pmatrix}a \\b \\c\end{pmatrix} = {\begin{pmatrix}{\sum x_{i}^{4}} & {\sum x_{i}^{3}} & {\sum x_{i}^{2}} \\{\sum x_{i}^{3}} & {\sum x_{i}^{2}} & {\sum x_{i}} \\{\sum{x2}} & {\sum x_{i}} & n\end{pmatrix} \cdot {\begin{pmatrix}{\sum{x_{i}^{2}y_{i}}} \\{\sum{x_{i}y_{i}}} \\{\sum y_{i}}\end{pmatrix}.}}$

An alternative analytic curve that provides better conformance to thedata characteristics is the exponential, such as a Gaussian. A simplemethod for performing a Gaussian-like fit is to assume that the form ofthe curve is given by y=e^(ax) ² ^(+bx+c), in which case the quadraticequations above can be utilized by forming y′, where y′=lny. Theexponential provides a better fit, providing a 20% improvement over thatof the quadratic fit.

Assuming that the exponential curve is the preferred data fittingmethod, the robustness of the curve fit is examined in two ways: withrespect to shifts in the wavelength and with respect to errors in thesignal amplitude.

To examine the sensitivity of the analytical peak location to the choiceof windows, the window from which the curve fitting is performed isaltered to fall 10 sampling intervals to the left or to the right of thetrue maxima. The resulting shift in mathematically-determined peaklocation is shown in Table 1. The result is that the peak location isreasonably robust with respect to the particular window chosen: for ashift of ˜1.5 nm, the corresponding peak location changed by only <0.06nm, or 4 parts in one hundred sensitivity.

TABLE 1 Comparison of peak location as a function of window locationShift Window Peak Location Δ = −10 bins 771.25–782.79 nm 778.8221 nm Δ =0 bins 772.70–784.23 nm 778.8887 nm Δ = + 10 bins 774.15–785.65 nm7778.9653 nm

To examine the sensitivity of the peak location with respect to noise inthe data, a signal free of noise must be defined, and then incrementalamounts of noise added to the signal, while the impact of this noise onthe peak location is examined. The ideal signal, for purposes of thisexperiment, is the average of 10 resonant spectra acquisitions.

Gaussian noise of varying degrees is superimposed on the ideal signal.For each such manufactured noisy signal, the peak location is estimatedusing the 2^(nd)-order exponential curve fit. This is repeated 25 times,so that the average, maximum, and minimum peak locations are tabulated.This is repeated for a wide range of noise variances—from a variance of0 to a variance of 750. The results show that this embodiment of peakdetection is extremely robust with respect to random, additive noise.The average peak location, under the range of variances examined, variedby 0. 1 nm about the idealized (i.e., noiseless) solution.

One preferred algorithm for mathematically determining the peak locationof a calorimetric resonant biosensor is as follows:

-   -   1. Input data x_(i) and y_(i), i=1, . . . , n    -   2. Find maximum        -   a. Find k such that y_(k)≧y_(i) for all i≠k    -   3. Check that maximum is sufficiently high        -   a. Compute mean y and standard deviation σ of sample        -   b. Continue only if (y_(k)− y)/σ>User Threshold    -   4. Define curve-fit region of 2w+1 bins (w defined by the user)        -   a. Extract x_(i), k−w≦i≦k+w        -   b. Extract y_(i), k−w≦i<k+w    -   5. Curve fit        -   a. g_(i)=ln y_(i)        -   b. Perform 2^(nd)-order polynomial fit to obtain g_(i)            defined on x_(i), k−w≦i≦k+w        -   c. Polynomial fit returns coefficients a, b, c of form            ax²+bx+c        -   d. Exponentiate: y′_(i)=e^(g′) ^(i)    -   6. Output        -   a. Peak location p given by x_(p)=−b/2a        -   b. Peak value given by y′_(p)(x_(p))

Resonance Peak Shift Detection Using Correlations

An alternative preferred method of determining the resonance peak shiftutilizes a correlation process. Using this method, a cross-correlationis performed between a set of reference spectral data and spectralmeasurements taken from one or more exposed biosensor wells. Acorrelation filter in the form of an FIR digital filter preferablyperforms the correlation. As one of ordinary skill in the art willappreciate, the correlation operation may be considered as an FIRdigital filtering operation, where the coefficients of the FIR filterare the reverse-ordered sample spectrum values. The output of the filterprovides an indication of the amount of shift that has occurred in thebiosensor reflectivity due to exposure to a sample under test.Specifically, the peak output of the filter provides an offset parameterthat indicates the amount of shift that has occurred in the spectralmeasurements. The amount of shift is related to the activity of thebiosensor, thereby providing a measurement from the biosensortransducer.

The correlation method may provide improved results compared to thecurve-fitting methods described above. The correlation method isparticularly well suited to new generations of GMRFB biosensors thattypically yield much sharper (i.e., narrower) resonance peaks.Specifically, presently available biosensors provide far fewer pointswith which to perform the curve fitting over the peak region. Inaddition the resonance spectra may be highly asymmetrical, also makingcurve fitting less reliable. Finally, the spectra may not exhibit astrong peak under certain conditions, also rendering curve-fitting peakfinding algorithms less accurate.

The cross correlation between ƒ(x) and g(x) is defined in the continuousdomain by

f(x) ⊗ g(x) = ∫_(−∞)^(∞)f(α)g(x + α)𝕕α,

where α denotes the lag of the correlation. The preferred embodiment isto utilize a normalized cross correlation function, where the integralis normalized by the product of the areas of ƒf(x) and g(x). In thiscase, the maximum correlation value is restricted to <=1. For sampleddata, the following relationship for the cross correlation r_(fg) offunctions ƒ and g, is used:

$\begin{matrix}{{{r_{fg}(i)} = {{{f(n)} \otimes {g(n)}} = {\sum\limits_{j}{{f(j)}{g\left( {j + i} \right)}}}}},} & \text{(Equation~~1)}\end{matrix}$

where i denotes the lag of the correlation, and the summation is overthe range of j where the functions are defined, or nonzero.Specifically, the values of g(n) may be the measured spectrum of theexposed biosensor, and the values of ƒ(n) may be the reference spectrumof the biosensor (the samples would be arranged in reverse order ifconventional FIR filtering equations are used). As discussed above, thesummation may be normalized by, e.g., the sum of all ƒ values and thesum of all g values.

In an alternative embodiment, only a portion of the spectrum may be usedin the cross correlation function. Specifically, only the portions nearthe peak need be included. As seen in FIG. 6, exemplary spectral dataare displayed. The most pertinent component of the spectral data is thepeak of the response. As shown in FIG. 6, one embodiment may use therange between 800 and 900 nanometers. As with the curve-fittingembodiment, the ranges may be determined using any suitable criteria,such as a predetermined range of wavelengths on either side of theabsolute maximum peak value, or a range of wavelengths based on amultiple of the half power bandwidth, turning points, user input, etc.

Using the relation given in equation 1, if the reference data isrepresented by ƒ(n) and the test data is represented by g(n), then g(n)is shifted to the left for positive i, and shifted right for negative i.In this manner, the index i corresponding to the peak output of thefilter (the value of i where r_(fg)=max(r_(ƒg)(i))) indicates thewavelength shift of the spectrum, with positive values indicating anincrease in wavelength (decrease in frequency), and negative valuesindicating a decrease in wavelength (or increase in frequency). Becausethe wavelengths are linearly spaced, the index may be converted into achange-in-wavelength value by multiplying the index by the samplinginterval. A typical correlation output is shown in FIG. 8, having a peakvalue at an offset (the offset corresponding to a peak correlation valuemay be referred to as a lag parameter) of approximately 136 samples. Inthe example of FIG. 8, each sample represents 0.01 nanometers, thusindicating a peak resonance shift of 1.36 nanometers. Thus, the lagparameter may be expressed in terms of samples, or alternatively interms of wavelength values.

Alternatively, the output of the correlation filter may be interpolatedto find a peak offset that may lie between integer multiples of thesampling interval. In this embodiment, the correlator output is providedto an interpolation routine, such as a piecewise cubic Hermiteinterpolation routine or other suitable routine as discussed previously.After performing cross correlation, the resulting correlation curve is awell-behaved, highly symmetrical function. To fit a curve to theresulting correlation function, numerous analytical functions can beused, including polynomial and exponential curves. One preferredembodiment is to utilize a quadratic curve, since quadratics are fast tocompute, and the resulting fit is of high quality.

Reference data is first obtained from the probe to determine thespectral reflectivity of the biosensor prior to exposure of thebiosensor to the sample under test. A plurality of measurements may bemade and the results averaged to represent the reference spectrum.Additionally, numerous wells may be used for a given test, and thereference data may be calculated for each well, or the data may beaveraged over some or all of the wells to obtain a reference spectrum.The reference spectra (or spectrum) are then used as filter coefficientsin the correlation filter, (e.g., ƒ(n)).

After the biosensor is exposed to the sample under test, the opticalprobe and spectrometer are used to collect spectral data. The crosscorrelation can be utilized in a variety of ways. In a sequence of nspectra, where n is large, one can correlate the reference spectrumagainst all n spectra. The results may then be averaged. If the rate ofa reaction conveys useful information, sample data may be taken atspecific intervals, or may be time stamped with the time of datacollection. The correlation results may then be analyzed, and theresonant frequency shift may then be plotted as a function of time.

In situations where the time aspects of the biosensor measurements arebeing analyzed, a series of spectral measurements may be made over aperiod of time to accommodate a temporal analysis of the reaction understudy. In some circumstances the spectral characteristics of thebiosensor other than the location of the peak resonance may changesignificantly from measurement to measurement. This makescorrelation-based peak finding somewhat less reliable when the measuredspectral data are correlated against a single reference spectrum.Alternatively, the measured spectra may be correlated in a daisy-chainfashion, such that each correlation is performed pair-wise. That is, incases in which the spectral variations or distortions may be severe, acascade of correlations can be used, where the 1st spectrum iscorrelated against the 2nd, the 2nd against the 3rd, and so on. Eachsuch correlation thus provides a measurement of an incremental shift foreach time period between corresponding measurements. The total shift maybe obtained by summing the incremental shift values. The offsets may beplotted and analyzed to determine kinetic trends, characteristics and/orrelationships.

Similarly, a mid-point spectrum may be used as a reference spectrum tocorrelate against all other measured data sets. Again, because thespectral shape may vary from the beginning of the measurements to thefinal measurement, a middle spectrum (the n/2-th spectrum, or othermid-point spectrum selected from a plurality of measured spectra) can beused as the reference spectrum in the correlation filter because itsspectral shape is likely more similar to the beginning and end spectra.In this embodiment, each correlation will provide offset measurements ofthe corresponding sampled spectra. The offsets may be plotted andanalyzed to determine kinetic relationships. The overall spectral shiftmay be obtained by adding the peak shifts of two correlations: themid-point spectrum correlated with the beginning spectral measurement(or the negative of the correlation) and the mid-point spectrumcorrelated with the final spectral measurement.

Correlation results may be further analyzed using the techniquesdescribed above to find a correlation peak. After performing crosscorrelation, the resulting correlation curve is a well-behaved, highlysymmetrical function. To fit a curve to the resulting correlationfunction, numerous analytical functions can be used, includingpolynomial and exponential curves. One preferred embodiment is toutilize a quadratic curve, since quadratics are fast to compute, and theresulting fit is of high quality. The curve characteristics may then beused to determine the correlation peak.

Resonance Peak Shift Detection Using Resonance Band Edges

In an alternative embodiment, the shift in resonance wavelength may bedetermined by analyzing the edges of the peak bandwidth. One techniqueto determine the edges is simply the 3 dB points (where the power is onehalf of the peak value). Other power levels may also be used, such as,e.g., the 1.25 dB points (three-quarter power), or the 6 dB points(one-quarter power). Alternative techniques generally include analyzingthe derivative of the spectral data waveform. Specifically, the positiveand negative peak values of the derivative are indicative of the upperand lower edges of the spectral peak, since these areas exhibit thegreatest amount of change per unit wavelength. A plot 900 of typicalderivative values is shown in FIG. 9. As can be seen in the Figure, thesample band edges may be determined by first determining an uppermaximum 904 and lower maximum 902 of the derivative of the measuredsample spectrum, where the upper maximum 904 is the largest negativevalue of the derivative, and the lower maximum 902 is the largestpositive value of the derivative. The sample band edges may then bedetermined as the wavelengths corresponding to the upper and lowermaximum of the derivative of the measured sample spectrum.

Alternatively, the derivative values may be weighted by the signalamplitude. In one embodiment, the derivative values may be divided bythe signal amplitude, or by the square of the signal amplitude. Infurther alternative embodiments, the derivative values may be multipliedby the signal amplitude, or by the square of the signal amplitude. Thechoice of the scaling factor to use, if any, may be made based on manyconsiderations, including modeling assumptions, and of course, actualperformance accuracy based on test data. This technique thus provides ameasure of the peak resonance offset based in part on the derivative ofthe sampled spectra, and the signal amplitude.

Alternatively, the sample band edges may be determined to be the upperand lower wavelengths where the spectrum values are one half the maximumspectral value. As shown in FIG. 9, the points that lie within thehalf-power bandwidth are very close to the same points that lie betweenthe upper and lower maxima of the derivative.

Once located using one or more of these techniques, the edges of thesampled spectrum may be compared to the reference spectrum. The shiftmay be determined by averaging the difference between the two lower bandedges (one reference, and one sample) and the difference between the twoupper band edges (again, one reference, and one sample). Alternatively,the absolute values of the differences may be used. Other techniques ofdetermining spectral shifts using resonance band edges may also be used.

Resonance Peak Shift Detection Using Maximal Likelihood Estimation

An alternative preferred embodiment is to utilize both amplitude andedge information in the determination of a spectral shift. An example ofthis embodiment can be derived from using a maximum likelihood estimator(MLE). The MLE can incorporate various assumptions, includingsignal-dependent and signal-independent noise models. A specificimplementation utilizing the model that the observed signal x(λ) issampled at different wavelengths λ_(i), in which the observationdeviates from the model by an unknown wavelength shift θ and corruptedby signal dependent noise w(λ), this model can be written as:y(λ_(i))=x(λ_(i)−θ)+w(λ_(i)).

In view of this model, values for x(λ_(i)) may be the reference spectrumobtained from the unexposed biosensor, and values for y(λ_(i))correspond to the spectral measurements from the exposed biosensor.Additional assumptions, such as the noise (w(λ_(i))) having the propertyof being characterized by being independently and identicallydistributed normal distribution with a mean of 0 and a variance of σ_(i)², or a Poisson distribution with variance σ_(i) ², where σ_(i) ², whereσ_(i) ²=G x(λ_(i)−θ) and G represents the gain of the system.

To compute the optimal value for θ, or equivalently to compute theoptimal estimation of the amount of shift, under these modelingassumptions, the optimality condition is obtained by setting thederivative of the corresponding cost function to zero, resulting in thefollowing equation:

$\begin{matrix}{0 = {\sum\limits_{i = 1}^{N_{\lambda}}{\frac{\left\lbrack \left. {- \frac{\mathbb{d}{x(\lambda)}}{\mathbb{d}\lambda}} \right|_{\lambda = {\lambda_{i}\mspace{14mu}\theta}} \right\rbrack}{\sigma_{i}^{2}}\left\lbrack {y_{i} - {x\left( {\lambda_{i} - \theta} \right)}} \right\rbrack}}} & \text{(equation~~2)}\end{matrix}$

In particular, note that the right-most bracketed term[y_(i)−x(λ_(i)−θ)] denotes the error associated with the fit of themodel. The error is then weighted by the bracketed term in thenumerator, which denotes the slope of the signal, and the term in thedenominator, which denotes the signal variance, which empiricalobservations of the model indicate is proportional to signal amplitude.Specifically, the system gain parameter G relating the signal amplitudeto the noise variance may be estimated off-line by taking numerousreference spectrum measurements, and for each wavelength, determining amean and a variance of the signal measurement. The system measurements,which include the signal of interest plus the noise component, may bemodeled as a wavelength-dependent Poisson process z(λ_(i))=Gv(λ_(i)).where v(λ_(i)) is Poisson. The mean, m_(z)(λ_(i))=Gm_(v)(λ_(i))), isrelated to the variance, σ_(z) ²=(λ_(i))=G² m _(v)(λ_(i)), by the factorG. Thus, G may be obtained by plotting the calculated means versusvariances and determining the slope that best fits the graph. Then,because the signal mean is also the value of the reference spectrumx(λ_(i)), the variance of the noise w(λ_(i)) associated withmeasurements of y(λ_(i)) may be estimated by σ_(i) ²=Gx(λ_(i)−θ). Notethat since Poisson distributions can be approximated by Gaussiandistributions when the sample size is large—which is indeed the case inthis embodiment of a biosensor, the modeling assumptions in equation 2remain valid. The gain will vary among systems, and is typicallydependent upon the spectrometer, biosensor and other conditions. Tosolve equation 2, one technique is to linearize equation 2 using aTaylor series expansion. The first two terms of the expansion representa linearized problem which may then be used to iteratively solve for θby computing values of Δθ^(k) in accordance with:

$\begin{matrix}\begin{matrix}{{\Delta\;\theta^{k}} = {\arg\;{\min\limits_{\Delta\;\theta}{{\begin{bmatrix}{\overset{\sim}{y}}_{1} \\\vdots \\{\overset{\sim}{y}}_{N_{\lambda}}\end{bmatrix} - {\begin{bmatrix}\left. \frac{- {\mathbb{d}{x(\lambda)}}}{\mathbb{d}\lambda} \right|_{\lambda = {\lambda_{i} - \theta_{k}}} \\\vdots \\\left. \frac{- {\mathbb{d}{x(\lambda)}}}{\mathbb{d}\lambda} \right|_{\lambda = {\lambda_{N_{\lambda}} - \theta_{k}}}\end{bmatrix}\Delta\;\theta}}}_{R^{- 1}}^{2}}}} \\{{\overset{\sim}{y}}_{i} = {{y\left( \lambda_{i} \right)} - {x\left( {\lambda_{i} - \theta^{k}} \right)}}} \\{R = {{diag}\left\lbrack \sigma_{i}^{2} \right\rbrack}}\end{matrix} & \text{(equation~~3)}\end{matrix}$

Specifically, the values of y(λ_(i)) are the measured spectral data froman exposed biosensor; x(λ_(i)) are the reference spectra; x(λ_(i)−θ_(κ))is the reference spectra shifted by an amount equal to an offsetestimate at time k, θ_(κ); and R⁻¹ is the inverse of the covariancematrix of the noise. In the formulation defined in Equation 3, asdiscussed above, the noise at each wavelength is modeled as independentnoise, and as such R is a diagonal matrix with the diagonal elementscorresponding to the noise in each wavelength channel.

Equation 3 represents a set of linear equations in the form of astandard linear least squares optimization problem. The solution may beobtained using well-known algorithms for the solution of least squaresproblems. One such solution involves the use of Moore-Penrose pseudoinverse solutions. Other solutions may also be used, such as conjugategradient, Gaussian elimination, etc., as will be recognized by those ofordinary skill in the art.

One preferred embodiment of the ML estimator is used by solving equation3 to determine an update Δθ^((k)) based on equations linearized aroundθ^((k)), using a least squares criterion. The estimate of the spectraloffset is then updated by adding Δθ^((k)) to the previous estimate:θ^((k+1))=θ^((k))+Δθ^((k)). The accuracy of the estimate of θ^((k)) maybe enhanced in an iterative manner, by determining a new update based onthe revised estimate θ^((k+1)). The ML estimator thus provides a measureof the peak resonance offset based in part on the derivative of thereference spectrum, and the reference spectrum and sample spectrumsignal amplitudes. Alternatively, the peak resonance offset is based inpart on the derivative of the reference spectrum, and measurements orother estimates of the signal-dependent noise.

As will be understood by those of ordinary skill in the art, the MLestimator described above may be modified to accommodate alternativesignal models or alternative assumptions. As one example of a modelingvariation, one may wish to consider that the reference spectrum as ashifted version of the measured spectrum from the exposed biosensor. Inthis manner, the roles of the reference spectrum and the measuredspectrum are reversed, and the estimation is performed in response tothe slope of shifted versions of the measured spectrum, rather thanshifted versions of the reference spectrum. Similarly, the estimation ofσ_(i) ² may be based on the measured spectrum, resulting in an MLestimator that provides a measure of the peak resonance offset based inpart on the derivative of the measured sample spectrum from an exposedbiosensor, and the signal amplitude of the measured spectrum.Furthermore, it should be understood that any suitable model may be usedto derive alternative ML estimators for use in determining biosensorpeak resonance offsets.

Thus, in a preferred embodiment, an iterative ML shift estimationapproach is used. Preferably, it operates on data points in the peakregion. The peak region contains points of high slope, typically about30–100 data points. The peak region may be determined using the methodspreviously described, such as a predetermined range of wavelengths oneither side of the absolute maximum peak value, or a range ofwavelengths based on a multiple of the half power bandwidth, turningpoints, user input, etc.

A method 1000 for detecting spectral resonance shifts will now bedescribed with reference to FIG. 10. At step 1002, a reference spectrumis determined. The reference spectrum may be obtained by one or moredirect measurements, or a prototypical reference spectrum may be used.This step may include determining reference band edges of the biosensorreference spectrum. At step 1004, the sample spectrum is measured. Atstep 1006, the band edges of the sample spectrum are obtained. The bandedges of the sampled spectrum may be referred to as sample band edges.

The sample band edges may be determined by first determining an upperand lower maximum of the derivative of the measured sample spectrum,where the upper maximum is the largest negative value of the derivative,and the lower maximum is the largest positive value of the derivativeThe sample band edges may then be determined as the wavelengthscorresponding to the upper and lower maximum of the derivative of themeasured sample spectrum.

Alternatively, the sample band edges may be determined to be the upperand lower wavelengths where the spectrum values are one half the maximumspectral value. The reference band edges may be referred to as a lowerreference band edge and an upper reference band edge, and the sampleband edges may be referred to as a lower sample band edge and an uppersample band edge.

As a further alternative, the sample band edges may be determined to bethe upper and lower turning points, which are the wavelengthscorresponding to the turning points associated with the edges of theresonance peak. Step 1006 may optionally include an interpolation stepto provide linearized data samples prior to band edge analysis.

At step 1008 the spectral offset is determined in response to the changein the locations of the band edges of the reference spectrum and themeasured spectrum (i.e., the change in the reference band edges and thesampled band edges). The step of determining an offset may includeaveraging the difference between the lower reference band edge and thelower sample band edge and the difference between an upper lowerreference band edge and an upper sample band edge.

An alternative preferred method 1100 for detecting spectral resonanceshifts will now be described with reference to FIG. 11. At step 1102, areference spectrum is determined. The reference spectrum may be obtainedby one or more direct measurements, or a prototypical reference may beused. At step 1104, the sample spectrum is measured. At step 1106, thesample spectrum and the reference spectrum are correlated. This mayinclude performing a singles correlation or a plurality of correlations,as discussed above. The choice of the reference spectrum to use in thecorrelations is also variable among the various embodiments describedherein. Further, this step may optionally include an interpolation stepto provide linearized data samples prior to correlation. At step 1108the spectral offset is determined in response to the correlation. Thismay optionally include curve fitting or interpolation to locate the peakof the correlation output and the corresponding lag parameter.

A method 1200 of spectral peak shift detection is depicted in the flowchart of FIG. 12. In this embodiment, the peak shift detection isperformed by using the linearized solution (equation 3) defined above,and initializing the beginning offset to zero by setting θ⁰=0 at step1202, then estimating an update Δθ^((k)) based on equations linearizedaround θ^((k)) at step 1204. Alternatively, the initialization step maybe performed by setting θ⁰ equal to some other value. Specifically, theinitial value may be determined by the peak finding method or thecorrelation method described above, or according to other criteria, suchas anticipated offset values, etc. The estimate of the spectral offsetis then updated at step 1206 by determining an offset update valueΔθ^((k)), and adding it to the previous estimate:θ^((k+i))=θ^((k))+Δθ^((k)). The accuracy of the estimate of θ^((k)) maybe enhanced by iteratively performing steps 1204 and 1206 until theestimate converges sufficiently. Sufficient convergence may bedetermined by the magnitude of the calculated value of Δθ^((k)), i.e.,Δθ^((k)) is below a predetermined threshold.

The peak shifting methods and apparatus described herein areparticularly useful in combination with a biosensor having a one, two,or three dimensional grating, typically made of a material having a highrefractive index (e.g., zinc sulfide, titanium dioxide, tantalum oxide,and silicon nitride). The grating is preferably formed on a substratelayer (e.g., glass, plastic or epoxy) to support the grating. Thegrating preferably has a period of about 0.01 microns to about 1 micronand a depth of about 0.01 microns to about 1 micron. The biosensorpreferably includes one or more specific binding substances (e.g.,nucleic acids, polypeptides, antigens, polyclonal antibodies, monoclonalantibodies, single chain antibodies (scFv), F(ab) fragments, F(ab′)₂fragments, Fv Fragments, small organic molecules, cells, viruses,bacteria, and biological samples) are immobilized by e.g., physicaladsorption or by chemical binding, on the surface of the gratingopposite of the substrate layer. Alternatively, there may be a coverlayer (typically a material that has a lower refractive index than zincsulfide, titanium dioxide, tantalum oxide, and silicon nitride, such asglass, epoxy, and plastic) on the surface of the grating and the bindingsubstances are immobilized on the surface of the cover layer.

In use, the biosensor is illuminated, and a resonant grating effect isproduced on the reflected radiation spectrum. Further, the depth andperiod of the grating are less than the wavelength of the resonantgrating effect. The biosensor reflects a narrow band of opticalwavelengths when the biosensor is illuminated with a broad band ofoptical wavelengths. Typically the bandwidth of the resonance peak is inthe range of 1–3 nanometers. Such narrow resonance peaks make peakdetection (and hence peak offset detection) considerably more difficultthan spectra produced from other biosensor structures.

A preferred embodiment of the present invention has been describedherein. It is to be understood, of course, that changes andmodifications may be made in the embodiments without departing from thetrue scope of the present invention, as defined by the appended claims.The present embodiments preferably include logic to implement thedescribed methods in software modules as a set of computer executablesoftware instructions. The Computer Processing Unit (“CPU”) ormicroprocessor implements the logic that controls the operation of thesystem. The microprocessor executes software that can be programmed bythose of skill in the art to provide the described functionality.

The software can be represented as a sequence of binary bits maintainedon a computer readable medium including magnetic disks, optical disks,and any other volatile or (e.g., Random Access memory (“RAM”))non-volatile firmware (e.g., Read Only Memory (“ROM”)) storage systemreadable by the CPU. The memory locations where data bits are maintainedalso include physical locations that have particular electrical,magnetic, optical, or organic properties corresponding to the storeddata bits. The software instructions are executed as data bits by theCPU with a memory system causing a transformation of the electricalsignal representation, and the maintenance of data bits at memorylocations in the memory system to thereby reconfigure or otherwise alterthe unit's operation. The executable software code may implement, forexample, the methods as described above.

It should be understood that the programs, processes, methods andapparatus described herein are not related or limited to any particulartype of computer or network apparatus (hardware or software), unlessindicated otherwise. Various types of general purpose or specializedcomputer apparatus may be used with or perform operations in accordancewith the teachings described herein. The use of C, C+, C++, Matlab,Mathcad, or other suitable software languages may be used to implementthe signaling processing functions and other aspects of the systemsdescribed herein. Furthermore, the system may utilize wirelesscommunication systems, and involve portable handheld devices.

In view of the wide variety of embodiments to which the principles ofthe present invention can be applied, it should be understood that theillustrated embodiments are exemplary only, and should not be taken aslimiting the scope of the present invention. For example, the steps ofthe flow diagrams may be taken in sequences other than those described,and more or fewer elements may be used in the block diagrams.

It should be understood that a hardware embodiment might take a varietyof different forms. The hardware may be implemented as an integratedcircuit with custom gate arrays or an application specific integratedcircuit (“ASIC”). Of the course, the embodiment may also be implementedwith discrete hardware components and circuitry.

The claims should not be read as limited to the described order ofelements unless stated to that effect. In addition, use of the term“means” in any claim is intended to invoke 35 U.S.C. §112, paragraph 6,and any claim without the word “means” is not so intended. Therefore,all embodiments that come within the scope and spirit of the followingclaims and equivalents thereto are claimed as the invention.

1. A method for determining biosensor resonance peak offsets comprising the steps: (i) determining a reference spectrum and a sample spectrum, the reference spectrum having a magnitude and a slope; and, (ii) determining a peak resonance offset in response to the slope of the reference spectrum.
 2. The method of claim 1 wherein the step of determining a peak resonance offset comprises determining an offset that minimizes a criteria for a set of linear equations, wherein each linear ecluation represents the difference between an error term and the product of the slope with a phase shift update, Δθ.
 3. The method of claim 1 wherein the step of determining a peak resonance offset comprises determining reference band edges in response to the slope of the reference spectrum weighted by the signal amplitudes of the reference spectrum, determining sample band edges in response to the slope of the sample spectrum weighted by the signal amplitudes of the sample spectrum, and determining a relative change in band edges between the reference spectrum and the sample spectrum.
 4. The method of claim 1 wherein the step of determining a peak resonance offset is performed by weighting the slope of the reference spectrum by the signal amplitudes of the reference spectrum.
 5. The method of claim 1 wherein the roles of the reference spectrum and the sampled spectrum are reversed, and the estimation is performed in response to the slope of shifted versions of the sampled spectrum.
 6. The method of claim 1, wherein the step of determining a peak resonance offset in response to the slope of the reference spectrum comprises the steps: (a) determining an initial offset estimate; (b) determining an offset update value; (c) updating the initial offset estimate in response to the offset update value.
 7. The method of claim 6 wherein steps (b) and (c) are repeated until a determined offset update value is below a predetermined threshold.
 8. The method of claim 6 wherein the step of determining an initial offset value is performed by one of the following steps: (a) determining an offset corresponding to a peak resonance value; (b) determining an offset corresponding to a peak correlation value; (c) determining an offset corresponding to a difference between measured band edges and reference band edges.
 9. The method of claim 6 wherein the offset update value is responsive to the derivative of the reference spectrum.
 10. The method of claim 6 wherein the offset update value is determined using a least squares criterion.
 11. The method of claim 6 wherein the offset update value is determined using a criterion based on maximal likelihood estimation.
 12. The method of claim 1 wherein the step of determining a peak resonance offset comprises performing an interative calculation to estimate spectral offset of the sample spectrum based on a maximal likelihood estimation, wherein each iteration is performed in response to the signal amplitude values of the reference spectrum and the sample spectrum and signal slope values of at least one of the reference spectrum and the measured spectrum.
 13. The method of claim 12 wherein the iterative calculation is performed until the spectral offset estimate has converged.
 14. The method of claim 12 wherein the iterative calculation uses signal values of one of the reference spectrum and the sample spectrum as estimates of noise values. 